I'm lost here. I found the vectors [1, 1, -1] and [-5, 4, -1] span the Kernel, but I really have no idea where to go from here... would it be the product of the matrices that have kernels in the two lines in the direction of the two vectors?

I'm lost here. I found the vectors [1, 1, -1] and [-5, 4, -1] span the Kernel, but I really have no idea where to go from here... would it be the product of the matrices that have kernels in the two lines in the direction of the two vectors?

You're in the right track! Now just define a lin. trans. T s.t. . For this, complete these two vectors to a basis of and then define the l.t. on the third vector to be anything but the zero vector, and extend by linearity.

Tonio

Pd. I'm assuming you meant the plane ...(Thinking)

Feb 2nd 2011, 09:36 AM

FernandoRevilla

Choose, for example, the basis of :

Then,

such that determines a family of linear transformations with the given kernel.

Sorry, we haven't covered the basis of a matrix/space, so completing a vector to a basis of |R3 doesn't mean anything yet.

Feb 2nd 2011, 10:02 AM

Lord Voldemort

Ok maybe not? I really don't know what you mean by completing something to a basis. Also as you said, "define the l.t. on the third vector to be anything but the zero vector", I don't understand how defining a new LT will do anything.

Feb 2nd 2011, 11:49 AM

FernandoRevilla

Quote:

Originally Posted by Lord Voldemort

Ok maybe not? I really don't know what you mean by completing something to a basis. Also as you said, "define the l.t. on the third vector to be anything but the zero vector", I don't understand how defining a new LT will do anything.

If you haven't covered the concept of matrix of a linear transformation with respect to determined basis, it is rather difficult to solve the above doubt.

There are alternatives to solve your problem, but we need to know what tools we can use.